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The codegree density gamma(F) is the limit of coex(n,F)/(n-2) as n tends to infinity.\n  In this paper we generalise a construction of Czygrinow and Nagle to bound below the codegree density of complete 3-graphs: for all integers s>3, the codegree density of the complete 3-graph on s vertices K_s satisfies gamma(K_s)\\geq 1-1/(s-2).\n  We also provid"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.3395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-12T10:24:42Z","cross_cats_sorted":[],"title_canon_sha256":"4b07e2d508605ce57ab9d21b295f519e194dde82d6f99d2d089a0b4a87735ab4","abstract_canon_sha256":"8a67af311649cec89cb0c82ab6a9585479bef99dfafb05a0bb1983d9a3abd6df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:39.249789Z","signature_b64":"eNUPHLY4WVUw+7Uzcd+g63LKSXamIRARD7KpzBwOG/YRXz4Waiy8i02lKEb0HWHfMTRYsuXq0Cp0k1XNraiLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c38f13dddde73e2670b500ea967dcfbb7df891cac45ad7f92c1d375517b8320e","last_reissued_at":"2026-05-18T03:18:39.249376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:39.249376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the codegree density of complete 3-graphs and related problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Victor Falgas-Ravry","submitted_at":"2013-07-12T10:24:42Z","abstract_excerpt":"Given a family of 3-graphs F its codegree threshold coex(n, F) is the largest number d=d(n) such that there exists an n-vertex 3-graph in which every pair of vertices is contained in at least d 3-edges but which contains no member of F as a subgraph. The codegree density gamma(F) is the limit of coex(n,F)/(n-2) as n tends to infinity.\n  In this paper we generalise a construction of Czygrinow and Nagle to bound below the codegree density of complete 3-graphs: for all integers s>3, the codegree density of the complete 3-graph on s vertices K_s satisfies gamma(K_s)\\geq 1-1/(s-2).\n  We also provid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3395","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.3395","created_at":"2026-05-18T03:18:39.249442+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.3395v1","created_at":"2026-05-18T03:18:39.249442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3395","created_at":"2026-05-18T03:18:39.249442+00:00"},{"alias_kind":"pith_short_12","alias_value":"YOHRHXO5447C","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YOHRHXO5447CM4FV","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YOHRHXO5","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN","json":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN.json","graph_json":"https://pith.science/api/pith-number/YOHRHXO5447CM4FVADVJM7OPXN/graph.json","events_json":"https://pith.science/api/pith-number/YOHRHXO5447CM4FVADVJM7OPXN/events.json","paper":"https://pith.science/paper/YOHRHXO5"},"agent_actions":{"view_html":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN","download_json":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN.json","view_paper":"https://pith.science/paper/YOHRHXO5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.3395&json=true","fetch_graph":"https://pith.science/api/pith-number/YOHRHXO5447CM4FVADVJM7OPXN/graph.json","fetch_events":"https://pith.science/api/pith-number/YOHRHXO5447CM4FVADVJM7OPXN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN/action/storage_attestation","attest_author":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN/action/author_attestation","sign_citation":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN/action/citation_signature","submit_replication":"https://pith.science/pith/YOHRHXO5447CM4FVADVJM7OPXN/action/replication_record"}},"created_at":"2026-05-18T03:18:39.249442+00:00","updated_at":"2026-05-18T03:18:39.249442+00:00"}